The weight two and opposite sign cases for the Fourier relative trace formulas

2026/03/13 by Matteo Di Scipio
#math.NT

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Abstract

We provide an adelic relative trace formula proof to the Petersson/Bruggeman-Kuznetsov (PBK) formulas, specifically in the holomorphic case for κ=2 and the non-holomorphic case for m₁m₂<0. Given two sets of hypothesis on the non archimedean test function f, called the geometric and spectral assumptions, this approach allows us to obtain refined PBK formulas.

Citations

• Primes in arithmetic progressions to large moduli

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